I found a very simple way to get evidence. From the courtroom, turn around and head straight into the room where the cop and the usher are talking. Fire an unsilenced Silverballer shot (from cover) at the door connecting this room to the one with evidence. Be careful not to let the usher even get a little suspicious or she'll detect you when you fire. Wait until all the cops are out of the evidence room. Walk in, get the evidence, get the keycard from the next room, leave. Simple as that!